Chapter 14, Problem 2E

a)

To determine

To find the sample space and explain whether the events are equally likely.

Answer to Problem 2E

Not equally likely events.

Explanation of Solution

Given:

Roll two dice; record the sum of the numbers.

The events are said to be equally likely if it has an equal chance being selected.

A die can take only values between 1 and 6. So, the sample space for the given events is,

  $S=\{2,3,4,5,6,7,8,9,10,11,12\}$

Therefore, it is more likely to roll a sum of 7 than it is to roll a sum of 2. Hence, events are not equally likely.

b)

To determine

To find the sample space and explain whether the events are equally likely.

Answer to Problem 2E

Equally likely events.

Explanation of Solution

Given:

A family has 3 children; record each child’s sex in order of birth.

The events are said to be equally likely if it has an equal chance being selected.

Let, B denote Boy and G denote girl. So, the sample space for the given events is,

  $S=\{BBB,BBG,BGB,BGG,GBB,GBB,GBG,GGG\}$

Therefore, there is an equal chance of boy or girl. Hence, events are equally likely.

c)

To determine

To find the sample space and explain whether the events are equally likely.

Answer to Problem 2E

Not equally likely events.

Explanation of Solution

Given:

Toss four coins; record the number of tails.

The events are said to be equally likely if it has an equal chance being selected.

In 4 coins, there is possibility of 0,1,2,3 and 4 tails. So, the sample space for the given events is,

  $S=\{0,1,2,3,4\}$

Therefore, there is more chance of having 2 tails than 0 tails. Hence, events are not equally likely.

d)

To determine

To find the sample space and explain whether the events are equally likely.

Answer to Problem 2E

Not equally likely events.

Explanation of Solution

Given:

Toss a coin 10 times; record the length of the longest run of heads.

The events are said to be equally likely if it has an equal chance being selected.

When tossing a coin10times, there is possibility of long run heads is between 1 to 10. So, the sample space for the given events is,

  $S=\{1,2,3,4,5,6,7,8,9,10\}$

Therefore,3 heads in a row is much more likely to occur than 10 heads in a row. Hence, events are not equally likely.